CAT 2020 Previous Year Question Paper

Passage 1

Histories of technology tend to be histories of invention. They celebrate the first telephone call, the first powered flight, the first transistor, and they measure progress by the arrival of new things. Far less attention goes to the work that keeps old things running: the inspection of bridges, the patching of water mains, the updating of software that nobody any longer finds exciting. Yet for most people, most of the time, the technologies that matter are not new ones. They are the ageing networks of pipes, wires and roads on which daily life quietly depends.

The neglect is not only a matter of historical taste. It shapes budgets. Public bodies find it easier to raise money for a new rail line, which can be opened with a ceremony, than for replacing the signalling equipment on an existing one, which produces nothing visible except the absence of failure. Private firms, too, reward the engineer who launches a product more readily than the one whose diligence prevents an outage. Maintenance is a service whose success is measured by what does not happen, and things that do not happen are hard to praise.

The consequences accumulate slowly and then appear suddenly. An under-maintained system does not decline smoothly; it goes on working, apparently normally, until a component fails and exposes a fragility that had been building for years. When the collapse comes, it is often described as an accident, as though nobody could have foreseen it. More often it was foreseen, by the very people responsible for maintenance, whose warnings were weighed against more glamorous demands and found lighter.

Some writers have responded by proposing that societies should celebrate maintainers as they celebrate innovators. The proposal is appealing but may misjudge the problem. Prestige matters less than the structures that allocate money and attention. If budgets reward new construction and treat the costs of upkeep as a drain, praise alone will change little. What is needed are accounting practices that make the deferred cost of neglect visible, so that postponing a repair shows up as a liability rather than as a saving.

There is, finally, a quieter argument for taking maintenance seriously. Innovation promises a future different from the present; maintenance assumes a future that resembles the present closely enough for existing arrangements to be worth preserving. In a period of anxiety about change, the second attitude may look merely conservative. But it is also a form of care, and a society that cannot look after what it already has is unlikely to make good use of whatever it invents next.

1. According to the passage, maintenance tends to be underfunded chiefly because

   1. engineers who do maintenance are less skilled than those who invent.
   2. its successes are invisible, and budgeting and reward structures favour visible new projects.
   3. old infrastructure no longer matters to most people.
   4. historians have persuaded governments that invention is more important.
   Answer and explanation

   Answer: B (its successes are invisible, and budgeting and reward structures favour visible new projects.)

   Paragraph two says a new line 'can be opened with a ceremony' while maintenance 'produces nothing visible except the absence of failure', and that budgets and firms reward launches. C contradicts paragraph one; D overstates the influence of historians, which the author calls 'not only a matter of historical taste'.

2. The author's response to the proposal that maintainers be celebrated like innovators is best described as

   1. enthusiastic endorsement, since prestige is the root of the problem.
   2. sympathetic but sceptical: praise will achieve little unless budgeting and accounting change.
   3. dismissive, because maintainers do not deserve recognition.
   4. neutral, since the author offers no view on it.
   Answer and explanation

   Answer: B (sympathetic but sceptical: praise will achieve little unless budgeting and accounting change.)

   The author calls the proposal 'appealing but may misjudge the problem', arguing that 'prestige matters less than the structures that allocate money and attention'.

3. In the third paragraph, the statement that the maintainers' warnings were 'weighed against more glamorous demands and found lighter' means that the warnings were

   1. judged less important than other, more attractive claims on resources.
   2. proved to be technically mistaken.
   3. ignored because they were written in unclear language.
   4. acted upon only after the collapse.
   Answer and explanation

   Answer: A (judged less important than other, more attractive claims on resources.)

   The metaphor of weighing means the warnings were compared with competing demands and given less priority, not that they were wrong (B).

4. Which of the following would best support the author's claim that collapses described as accidents were often foreseen?

   1. Records showing that maintenance staff warned in writing, years before a failure, about the component that later failed.
   2. Evidence that a bridge collapsed during an unprecedented earthquake.
   3. Reports that a new rail line was opened with a large public ceremony.
   4. Surveys showing that engineers who launch new products receive more bonuses.
   Answer and explanation

   Answer: A (Records showing that maintenance staff warned in writing, years before a failure, about the component that later failed.)

   The claim is that failures were anticipated by maintainers whose warnings went unheeded; documented prior warnings are direct evidence. B suggests a genuinely unforeseeable event; C and D concern the funding bias, not foresight.

Verbal ability

5. The five sentences below, labelled 1 to 5, form a coherent paragraph when properly ordered. Type in the correct order as a sequence of five numbers. 1. On a good day a single large net can gather enough water to meet a small community's drinking needs. 2. Villagers in such places have begun stretching fine mesh nets across hillsides that face the wind. 3. The method is cheap and needs no power, though it depends entirely on the fog continuing to arrive. 4. In some coastal deserts rain almost never falls, but fog rolls in from the sea on most mornings. 5. As the fog drifts through, droplets collect on the mesh, merge and trickle down into gutters below. (type in your answer)

   Answer and explanation

   Answer: 42513

   4 sets the scene (deserts with fog). 2 ('such places') introduces the nets. 5 explains how they collect water. 1 gives the yield. 3 evaluates the method. Order: 4-2-5-1-3.

6. Five sentences related to a topic are given below. Four of them can be put together to form a coherent paragraph. Identify the sentence that does not fit and type in its number. 1. Before the printing press, books were copied by hand, often in monasteries. 2. A single copy of a long work could take a scribe many months to finish. 3. Errors crept in with each copy, so that texts drifted further from their originals over time. 4. Scholars today compare surviving manuscripts to reconstruct the likely wording of lost originals. 5. A modern rotary press can print tens of thousands of newspapers in an hour. (type in your answer)

   Answer and explanation

   Answer: 5

   Sentences 1–4 trace hand-copying, the errors it introduced and how scholars correct for them. Sentence 5 is about the speed of modern newspaper printing and breaks the thread.

7. The passage given below is followed by four summaries. Choose the option that best captures the essence of the passage. Food labels that list calories per serving are meant to help shoppers make informed choices. But serving sizes are set by manufacturers, and a packet that most people finish in one sitting may be labelled as containing three servings. The figure on the label is accurate and yet misleading, because it describes a portion few people actually eat.

   1. A per-serving figure can be accurate yet misleading when the stated serving is smaller than what people actually eat.
   2. Manufacturers deliberately print false calorie figures on food labels.
   3. Shoppers ignore calorie labels when choosing food.
   4. Serving sizes should be removed from food labels altogether.
   Answer and explanation

   Answer: A (A per-serving figure can be accurate yet misleading when the stated serving is smaller than what people actually eat.)

   The passage stresses that the figure is 'accurate and yet misleading' because of unrealistic serving sizes. B contradicts 'accurate'; C and D are not stated.

Set 1

Five colleagues, A, B, C, D and E, each made one business trip during a particular week, on five different days from Monday to Friday, and to five different cities: Delhi, Pune, Goa, Agra and Kochi. The following is known:

1. A travelled on an earlier day than the colleague who went to Goa. 2. The trip to Kochi was on Wednesday. 3. B travelled on Friday, but not to Agra. 4. C went to Pune, on the day immediately after D's trip. 5. E did not go to Delhi, and E travelled on an earlier day than C.

8. Who went to Kochi?

   1. A
   2. C
   3. D
   4. E
   Answer and explanation

   Answer: C (D)

   B is on Friday. C is the day after D, and E is before C, so C cannot be Monday or Tuesday (Tuesday would put D on Monday and leave no day for E before C). If C were Wednesday, C's city would be Kochi, but C went to Pune. C cannot be Friday (B). So C is Thursday and D Wednesday, meaning D went to Kochi.

9. For how many of the five colleagues can both the day of travel and the city be determined with certainty? (type in your answer)

   Answer and explanation

   Answer: 2

   D (Wednesday, Kochi) and C (Thursday, Pune) are fixed. A and E take Monday and Tuesday in some order, and B (Friday) went to Goa or Delhi. The valid arrangements are: A Mon Delhi, E Tue Agra, B Fri Goa; A Mon Agra, E Tue Goa, B Fri Delhi; E Mon Agra, A Tue Delhi, B Fri Goa. So only C and D are fully determined: 2.

10. If the trip to Delhi was on Monday, who went to Goa?

    1. A
    2. B
    3. E
    4. Cannot be determined
    Answer and explanation

    Answer: B (B)

    Of the three valid arrangements, only A Mon Delhi, E Tue Agra, D Wed Kochi, C Thu Pune, B Fri Goa has Delhi on Monday. So B went to Goa.

11. Which of the following could be true?

    1. E went to Goa on Tuesday.
    2. A travelled on Wednesday.
    3. B went to Agra.
    4. C travelled on Tuesday.
    Answer and explanation

    Answer: A (E went to Goa on Tuesday.)

    E going to Goa on Tuesday occurs in the arrangement A Mon Agra, E Tue Goa, D Wed Kochi, C Thu Pune, B Fri Delhi, which satisfies every condition (A is before the Goa traveller). A is never on Wednesday, B never goes to Agra (condition 3) and C is always on Thursday.

12. A's salary is 25% more than B's. By what percentage is B's salary less than A's?

    1. 22.5%
    2. 25%
    3. 20%
    4. 15%
    Answer and explanation

    Answer: C (20%)

    If B earns 100, A earns 125. B is 25 less than 125, i.e. 25/125 = 20% less.

13. Two runners start together from the same point on a 400 m circular track and run in opposite directions at 5 m/s and 3 m/s. After how many seconds will they first be together again at the starting point?

    1. 400
    2. 50
    3. 200
    4. 1200
    Answer and explanation

    Answer: A (400)

    Lap times are 400/5 = 80 s and 400/3 s. They are both at the start at the first common multiple: 80 = 240/3 and 400/3, so the answer is LCM(240, 400)/3 = 1200/3 = 400 s (5 laps and 3 laps). Direction does not matter for meeting at the start.

14. How many ordered pairs of positive integers (x, y) satisfy x² − y² = 45? (type in your answer)

    Answer and explanation

    Answer: 3

    (x − y)(x + y) = 45 with both factors odd and x − y < x + y: (1, 45), (3, 15), (5, 9), giving (x, y) = (23, 22), (9, 6), (7, 2). So 3 pairs.

15. A chord AB of a circle of radius 6 cm subtends an angle of 120° at the centre. What is the length of AB?

    1. 6√3 cm
    2. 6 cm
    3. 6√2 cm
    4. 12 cm
    Answer and explanation

    Answer: A (6√3 cm)

    AB = 2r sin(120°/2) = 2 × 6 × sin 60° = 12 × (√3/2) = 6√3 cm.

16. The diagonal of a rectangle is 13 cm and its perimeter is 34 cm. What is its area in cm²? (type in your answer)

    Answer and explanation

    Answer: 60

    l + w = 17 and l² + w² = 169. Then 2lw = (l + w)² − (l² + w²) = 289 − 169 = 120, so the area lw = 60 cm² (the sides are 12 and 5).

17. How many zeros are there at the end of 125! (125 factorial)?

    1. 25
    2. 31
    3. 30
    4. 32
    Answer and explanation

    Answer: B (31)

    Count the factors of 5: ⌊125/5⌋ + ⌊125/25⌋ + ⌊125/125⌋ = 25 + 5 + 1 = 31.

18. The sum of an infinite geometric progression is 20 and the sum of the squares of its terms is 80. What is its first term?

    1. 4
    2. 5
    3. 20/3
    4. 8
    Answer and explanation

    Answer: C (20/3)

    a/(1 − r) = 20 and a²/(1 − r²) = 80. Dividing the second by the first gives a/(1 + r) = 4. So 20(1 − r) = 4(1 + r), r = 2/3 and a = 20 × (1/3) = 20/3.

19. A 40-litre mixture contains alcohol and water in the ratio 3 : 5. How many litres of alcohol must be added so that alcohol makes up half of the mixture? (type in your answer)

    Answer and explanation

    Answer: 10

    Alcohol = 15 L and water = 25 L. For equal quantities we need 25 L of alcohol, so add 10 L.

20. Given that log₁₀ 2 = 0.3010, how many digits does 2⁵⁰ have?

    1. 15
    2. 17
    3. 18
    4. 16
    Answer and explanation

    Answer: D (16)

    log₁₀(2⁵⁰) = 50 × 0.3010 = 15.05. The number of digits is ⌊15.05⌋ + 1 = 16.